Aydın Tiryaki

Dynamic Fixture Model (DFM): Performance and Fairness-Based League Management Algorithm (2006-2025)

Optimization of the Second Round in a Double Round-Robin League System

Aydın Tiryaki (2025)

I. INTRODUCTION AND OPERATIONAL CONSTITUTION

The Dynamic Fixture Model (DFM) is an “intelligent scheduling” structure that, following the traditional draw system in the first half of the league, adapts to team performance in the second half.

Immutable Fundamental Rules:

  • Implementation: The Dynamic Fixture Model is designed for the second half of a two-round league season.
  • Venue Symmetry: Every team plays two matches against each opponent during the season—one at home and one away. The home venue in the second half is the exact reciprocal of the first half. Each team completes the season with an equal number of home and away games.
  • Logistical Constraints: The model aims to minimize consecutive home or away sequences, typically limiting them to a maximum of two, though the model can be further optimized to reduce this.
  • Binary Block Pairing (CRITICAL): In this model, “neighborhood” is based on the principle of “Block Matching.” In 4-group setups, blocks (AB) and (CD) are fixed as “Neighboring Groups”; in 6-group setups, blocks (AB), (CD), and (EF) are fixed as “Neighboring Groups.” Group A can only combine with group B, group C only with group D, and group E only with group F to form a block.
  • Dynamic Reorganization: The process of merging and re-dividing neighboring blocks takes place in the week immediately preceding their encounter.
  • The Reserved Match: The match between the two highest-ranked teams in a group (e.g., A1-A2) is reserved for the final week to ensure maximum competitive excitement.
  • Stored Week: A period of matches shifted as a single unit to maintain scheduling symmetry. It serves as both a “planning” and “logistical” tool.

II. 24-TEAM MODEL (6×4 SETUP – 23 WEEKS)

  • Group Structure: 6 groups of 4 teams each (A, B, C, D, E, F).
  • Qualification Stage (Weeks 1-16): Groups play against groups outside their defined block neighbors.
    • (A and B play against C, D, E, F); (C and D play against A, B, E, F); (E and F play against A, B, C, D).
    • These matches are played in 4 periods of 4 weeks each:
    • Period 1: A-F; BD; CE
    • Period 2: A-E; BC; DF
    • Period 3: A-D; BE; CF
    • Period 4: A-C; BF; DE
  • Dynamic Reorganization (Beginning of Week 17): Fixed neighboring groups (A+B), (C+D), (E+F) merge. Based on the standings at the end of the Qualification Stage, each block of eight is further divided into “Upper” and “Lower” classification groups (4 teams each). These are then renamed (A, B, C, D, E, F).
  • Inter-Block Matches (Weeks 17-20): Two groups of four within the same block play against each other: A against B, C against D, E against F.
  • Intra-Group Decider Stage (Weeks 21-23): Four teams from each group are paired in a single round-robin format. The A1-A2 match (and equivalents in other groups) is reserved for the final week.
    • Week 21: A1-A4, A2-A3
    • Week 22: A1-A3, A4-A2
    • Week 23: A1-A2, A3-A4
  • Final (Week 23): The A1-A2 match determines the top of the league.

III. 20-TEAM MODEL (4×5 FORMATION – 19 WEEKS)

  • Group Structure: 4 groups of 5 teams each (A, B, C, D).
  • Qualification Stage (Weeks 1-10):
    • Period 1: A-C; BD
    • Period 2: A-D; BC
  • Dynamic Reorganization (Beginning of Week 11): Fixed neighboring groups (A+B) and (C+D) merge. In block AB, new “Upper Classification” (A1-A5) and “Lower Classification” (B1-B5) groups are formed based on the points table at the end of the Qualification Stage. Similarly, for block CD, new “Upper Classification” (C1-C5) and “Lower Classification” (D1-D5) groups are formed.
  • Inter-Block Matches (Weeks 11-14): Two groups of five within the same block play against each other (A vs B, C vs D). Only 4 of these 5 weeks are played; matches where A1-B1 (upper) and D5-C5 (lower) occur are reserved.
    • Week 11: A1-B5, A2-B1, A3-B2, A4-B3, A5-B4
    • Week 12: A1-B4, A2-B5, A3-B1, A4-B2, A5-B3
    • Week 13: A1-B3, A2-B4, A3-B5, A4-B1, A5-B2
    • Week 14: A1-B2, A2-B3, A3-B4, A4-B5, A5-B1
    • Hidden Week (Reserved): A1-B1, A2-B2, A3-B3, A4-B4, A5-B5
  • Intra-Group Decider Stage (Weeks 15-19): Single round-robin within groups. The team on a BYE plays its “Hidden Match” against the BYE team of the neighboring group (Ax vs Bx / Cx vs Dx).
    • AB Block:
    • Week 15: A1-B1, A5-A2, A4-A3, B5-B2, B4-B3
    • Week 16: A3-B3, A2-A4, A1-A5, B2-B4, B1-B5
    • Week 17: A5-B5, A4-A1, A3-A2, B4-B1, B3-B2
    • Week 18: A2-B2, A1-A3, A5-A4, B1-B3, B5-B4
    • Week 19: A4-B4, A3-A5, A2-A1, B3-B5, B2-B1
    • (A similar schedule is prepared for the CD block).
  • Final (Week 19): League concludes with A1-A2 and D4-D5.

IV. 18-TEAM MODEL (6×3 SETUP – 17 WEEKS)

  • Group Structure: 6 groups of 3 teams each (A, B, C, D, E, F).
  • Qualification Stage (Weeks 1-12): Inter-block matches in four 3-week periods.
  • Dynamic Reorganization (Beginning of Week 13): (A+B), (C+D), (E+F) merge and split into Upper/Lower tiers of 3 teams each.
  • Inter-Block Matches (Weeks 13-14):
    • Week 13: A1-B2, A2-B3, A3-B1
    • Week 14: A1-B3, A2-B1, A3-B2
    • Reserved Week: A1-B1, A2-B2, A3-B3
  • Intra-Group Decider Stage (Weeks 15-17): Single round-robin; BYE teams play their “Hidden Match” (Ax-Bx, Cx-Dx, Ex-Fx).
    • AB Block:
    • Week 15: A2-A3, B2-B3, A1-B1
    • Week 16: A1-A3, B1-B3, A2-B2
    • Week 17: A1-A2, B1-B2, A3-B3
  • Final (Week 17): Concludes with A1-A2 and F2-F3.

V. 16-TEAM MODEL (4×4 STRUCTURE – 15 WEEKS)

  • Group Structure: 4 groups of 4 teams each (A, B, C, D).
  • Qualification Stage (Weeks 1-8):
    • Period 1: A vs C, B vs D
    • Period 2: A vs D, B vs C
  • Dynamic Reorganization (Week 9): Merger of (A+B) and (C+D); Upper/Lower classification.
  • Inter-Block Phase (Weeks 9-12): A vs B, C vs D.
  • Intra-Group Decider Stage (Weeks 13-15):
    • Week 13: A1-A4, A2-A3
    • Week 14: A1-A3, A4-A2
    • Week 15: A1-A2, A3-A4
  • Final (Week 15): Concludes with A1-A2 and D3-D4.

VI. 12-TEAM MODEL (4×3 SETUP – 11 WEEKS)

  • Group Structure: 4 groups of 3 teams (A, B, C, D).
  • Qualification Stage (Weeks 1-6): Two 3-week periods (A-D, B-C; then A-C, B-D).
  • Dynamic Reorganization (Week 7): Formation of blocks (AB) and (CD); tiered into 3-team groups.
  • Inter-Block Phase (Weeks 7-8):
    • Week 7: A1-B2, A2-B3, A3-B1
    • Week 8: A1-B3, A2-B1, A3-B2
    • Reserved Week: A1-B1, A2-B2, A3-B3
  • Intra-Group Decider Stage (Weeks 9-11): BYE teams play “Hidden Matches” (Ax-Bx, Cx-Dx).
    • Week 9: A2-A3, B2-B3, A1-B1
    • Week 10: A1-A3, B1-B3, A2-B2
    • Week 11: A1-A2, B1-B2, A3-B3
  • Final (Week 11): Concludes with A1-A2 and D2-D3.

VII. 8-TEAM MODEL (4×2 SETUP – 7 WEEKS)

  • Group Structure: 4 groups of 2 teams (A, B, C, D).
  • Qualification Stage (Weeks 1-4): Inter-block play (A-C, B-D; then A-D, B-C).
  • Dynamic Reorganization (Week 5): Re-classification into Upper/Lower groups.
  • Inter-Block Phase (Weeks 5-6): A vs B, C vs D.
  • Final (Week 7): A1-A2, D1-D2.

VIII. BIBLIOGRAPHY AND REFERENCES

This model is built upon the author’s “Live Fixture” theory, published since 2006. While originally titled “Live Fixture,” the system has evolved into the “Dynamic Fixture Model” (DFM) to be more operationally user-friendly.

IMPORTANT CONCLUDING NOTE

This work presents a mathematically complete, operationally seamless, and turnkey framework for professional league management. The Dynamic Fixture Model (DFM) resolves the structural deficiencies of traditional systems and offers a reliable solution for both academic and practical applications.

The model is a universal solution, applicable not only to football but also to basketball, volleyball, handball, and any sport managed via a round-robin format. Ongoing research continues for specialized league structures, including odd-numbered teams and 22, 14, or 10-team configurations, which will be published in subsequent studies.

Aydın Tiryaki
Ankara, December 21, 2025

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